%% ============================================================
%  IM/DD Fading Notch – λ_null vs. Bandwidth (Fixed 10 km)
% ============================================================



%% Fiber and dispersion parameters
lambda0 = 1315e-9;   % Zero-dispersion wavelength [m]
S0      = 0.08;      % Dispersion slope at ZDW [ps/(nm²·km)]
L       = 10e3;      % Fiber length [m]
c       = physconst('lightspeed');

%% Frequency sweep (defines the desired first-fading notch)
f_targets = linspace(40e9, 150e9, 200);   % [Hz]
f_GHz = f_targets / 1e9;

%% Compute wavelength λ_null for each target f_null
[lambda_vec, Dacc_vec] = lambda_for_first_null_full(f_targets, L, lambda0, S0);
lambda_nm = lambda_vec * 1e9;   % Convert to nm

%% ------------------------------------------------------------
% Plot λ_null vs. f_null for 10 km fiber
% ------------------------------------------------------------
% figure('Color','w');
% plot(lambda_nm,f_GHz,  'LineWidth', 2);
% grid on; box on;

cols = cbrewer2('Paired',10);
figure('Color','w');hold on

plot(lambda_nm, f_GHz, 'LineWidth',2,'DisplayName',sprintf('%d km',L),'Color',cols(2,:));

yticks([56,75,90,112])

f_GHz = [56,75,90,112] * 1e9;
[lambda_vec, Dacc_vec] = lambda_for_first_null_full(f_GHz, L, lambda0, S0);
lambda_nm = lambda_vec * 1e9;   % Convert to nm

xticks(round(lambda_nm))

xlabel('$\Delta \lambda$ from ZDW [nm]');
ylabel('$F_{null}$  [GHz]');
grid on; box on;
lim=(lambda0.*1e9)-[8,40];
xlim([lim(2) lim(1)]);
% ylim([40,130])

%% ------------------------------------------------------------
% Helper function: lambda_for_first_null_full
% Stable, single-branch, clamped to O-band
% ------------------------------------------------------------
function [lambda_vec, Dacc_vec] = lambda_for_first_null_full(f_target, L, lambda0, S0)
c = physconst('lightspeed');
S0_si = S0 * 1e3;   % ps/(nm²·km) -> s/(m³)

% Define O-band boundaries [m]
lambda_min = 1260e-9;
lambda_max = 1360e-9;

f_target = f_target(:);
N = numel(f_target);

lambda_vec = zeros(N,1);
Dacc_vec   = zeros(N,1);

for k = 1:N
    RHS = c * 0.5 / (f_target(k)^2 * L);

    % Normal-dispersion branch (λ < λ0)
    fun = @(lambda) -(S0_si/4).*(lambda - (lambda0^4)./(lambda.^3)).*lambda.^2 - RHS;

    % Solve within normal-dispersion range
    try
        lambda_sol = fzero(fun, [lambda_min, lambda0 * 0.999]);
    catch
        lambda_sol = lambda_min;
    end

    % Clamp to O-band
    lambda_sol = min(max(lambda_sol, lambda_min), lambda_max);
    lambda_vec(k) = lambda_sol;

    % Compute D(lambda) and accumulated dispersion
    D_lambda = (S0_si/4) * (lambda_sol - (lambda0^4)/(lambda_sol^3)) / 1e-6; % ps/(nm·km)
    Dacc_val = D_lambda * (L/1000);                                          % ps/nm
    Dacc_val = min(max(Dacc_val, -100), 100);

    Dacc_vec(k) = Dacc_val;
end
end